The present invention relates to semiconductor photonic and opto-electronic devices. In particular, the present invention relates to an integrated optical wavelength multiplexers and demultiplexers and method of making the same.
Optical gratings are well known in the art and are used to disperse optical spectra spatially. Such gratings are commonly used in optical spectrometers to analyze the spectra composition of an optical beam. There is always a trade off between the length of an optical spectrometer and its resolution. Thus, if a higher wavelength resolution is required, the length required is also longer. Consider an example of a typical 1-meter long grating spectrometer in the market, which has a wavelength resolution of about Δλ=0.1 nm at λ=1000 nm or Δλ/λ=10−4. The dimensionless quantity for the length of the spectrometer L is L/λ and L/λ=106 in this example. The dimensionless product of the relative resolution Δλ/λ and the relative physical size L/λ of the spectrometer is dependent on the design of the spectrometer and in this example, spectrometer gives (Δλ/λ)×(L/λ)=100=RS. This factor (RS) in generally referred to as the “resolution vs size” factor. RS basically measures the compactness of a spectrometer for a given resolution power. The smaller the RS value, the more compact is the spectrometer. Only a few conventional spectrometers have RS factor less than about 10. This is primarily because of the various limitations in the current art (as will be described below).
It is known in the art that a relatively compact spectrometer can be achieved using a curved grating. The schematics of such a grating spectrometer is shown in FIG. 1A, illustrating an optical beam 1 entering an entrance slit 2 with slit size w1. The beam, after slit 2, undergoes wave diffraction towards a curved grating 3, which diffracts the beam spatially in a direction that is dependent on the optical wavelength of the beam. The curvature of the grating helps to refocus the diffracted beam to an exit slit 4 with slit size w2. Note that the term “exit slit” is also referred to as “outout slit” below so that the terms “exit slit” and “output slit” will be used totally interchangeably. Similarly, the terms “entrance slit” and “input slit” will be used totally interchangeably/Light through slit 4 is then detected by a photo detector 5. As is well known to those skilled in the art, the commonly used design for the curved grating 3 is the Rowland design. In the Rowland design, the grating has a circularly curved shape of radius R 6 and the slits SL1 and SL2 lie in a circle of radius R/2 7 as shown in FIG. 1A. The grating is ruled using a diamond tip with constant horizontal displacement d, which ruled the curved surface with constant Chord lines C1, C2, C3 and so forth, as shown in FIG. 1B. The segment lengths, S1, S2, S3 and so forth, along the curved surface are not a constant and vary along the curved surface.
Let the diffraction full angle from the entrance slit 1 be θdiv (defined by the angle of beam propagation at full-width half maximum (FWHM) of the beam intensity) As is well known to those skilled in the art, θdiv=2λ/d (in Radian). Let length L be the distance between the grating center and entrance slit 1, which is also approximately the distance between the grating center and the exit slit 4. As is well known to those skilled in the art, the resolution of the spectrometer increases with decreasing slit size w2. The imaging through the curved grating requires w1 and w2 to be about equal. A smaller slit size w1, however, leads to a larger diffraction angle θdiv. It can be shown that the Rowland design works reasonably well up to θdiv<4°. When θdiv>4°, the Rowland design could not give a sharp enough focus at the exit slit 4 (for Δλ<0.1 nm), thereby limiting the size of w2 and hence the resolution of the spectrometer. A diffraction angle of θdiv=4° corresponds to a slit size of about 25 microns (for λ=1000 nm). In the current art, it is typically difficult to make slit size smaller than 25 microns, and Rowland design is adequate for most present spectrometers with slit sizes larger than 25 microns.
Aberration Limitation:
In the case of the Rowland design, when θdiv>4 Degree(s) (DEG), serous aberration in the refocusing beam will occur to limit wavelength resolution. This is shown in FIG. 1C illustrating the ray tracing for the typical Rolwand-Echelle design at 4, 8, and 16 DEG diffraction. The ray tracing will allow us to see potential focusing distortion or aberration at the exit slit. In the figure, we show the focusing behavior for two sets of rays with wavelengths separated by 0.4 nm. From the figure, we see that their focused spots clearly separate when θdiv=4 DEG. However, when θdiv=8 DEG, the focused spots began to smear out. There is substantial distortion for the focusing rays when θdiv>4 DEG. Further simulations based on numerical solutions to Maxwell's wave equations using finite-difference time-domain (FDTD) method also show similar onset of focused spot size distortion at θdiv>4 DEG. In short, the current designs are close to their resolution-size (RS) limits at θdiv of about 4 DEG and cannot be made substantially more compact without losing wavelength resolution.
As discussed above, a curved-grating spectrometer is well specified by geometric configurations of its components as shown in FIG. 2. First, the location of the entrance slit; this is usually given by an θ1 with respect to the normal of the grating center and the distance S1 from the grating center. The center of the grating refers to the part of the grating hit by the center, i.e. high intensity point, of the entrance beam. Second, the locations of the first two grooves at the grating center; these are specified by its location vectors X1 and X(−1) with respect to the grating center as the origin of a two-dimensional (2-D) x-y coordinate system with coordinates (x,y)=(0,0). Let the 2-D vector at the origin be X0=(0,0) and its groove spacing (or pitch) d1=|X1−X0| and d−1=|X(−1)−X0|, where the 2-D vectors X1 and X(−1) are originated from or pointinging from X0 and are located symmetrically opposite to each other with respect to the grating center and therefore d=d1=d(−1). A circle can be defined by these three points X0, X1, and X2 and its radius is referred to as the radius of curvature at the grating center. Third, the location of the exit slit i.e. the location of the detector; this is specified by an angle θ2 with respect to the normal of the grating center and the distance S2 from the grating center. For a given operating wavelength center λc, the initial groove spacing d is usually chosen to satisfy the diffraction grating formula for a given entrance slit and detector location. The curved grating is further specified by the location of other grooves (specified by its location vector Xi, with respect to the grating center X0=(0,0) and the groove spacing di from the previous groove given by di=|XiXi−1|. Let the total number of grooves be N in each side of the grating center, the locus of all the grooves defined by the line that joins all tips of the vectors X(−N), . . . , X(−1), X0, X1, . . . , XN form a curved shape, which can lie in a circle or in any other curvilinear line. Curved shape of the grating acts as an imaging element of the spectrometer.
The shape of each groove centered at Xi is not critical to the resolution power of the grating and hence is not necessary to be a part of the main specification. However, the groove shape is related to the diffraction efficiency. For example, in order to increase the diffraction efficiency at a particular diffraction angle θ2, it is typically made a planar surface for each groove, oriented in such a way that it acts like a tiny mirror reflecting the input ray towards the angle θ2, a process typically referred to as blazing to angle θ2 (for a given wavelength λ). A section of each groove which reflects light is physically a two-dimensional surface of a particular shape, not a one-dimensional curve. However, the geometric shape of a groove is usually referred to as a one-dimensional curve of a particular shape. This is because there is no variation in the grating shape in the direction perpendicular to the plane where grating lies. Especially, spectrometers within a planar waveguide are strictly two-dimensional in their nature and the shape of grating or grooves will be referred with a curve, not with surface.
Conventional Rowland design spectrometers are specifically configured by the design rule described below in conjunction with FIG. 3.
Referring to FIG. 3, the entrance slit SL1 is located on a circle of R/2, where R is the radius of curvature of the grating at the grating center. This curvature at the grating center is called the grating-center curve. This circle of radius R/2 is called the Rowland circle and it is tangent to (i.e. passing through) the grating center. In the Rowland design, the distance S1 of the entrance slit to the grating center is related to the angle of incidence θ1 by S1=R*Cos(θ1), where “*” denotes numerical multiplication.
The detector is also located on the same Rowland circle as the entrance slit SL2. In the Rowland design, the distance S2 of the detector to the grating center is related to the angle of diffraction θ2 by S2=R*Cos(θ2).
During operation, an input light beam from the entrance slit will propagate to the grating and the different frequency components of the light beam will be dispersed by the grating to different directions. Part of the dispersed light then propagates to the output detector. The medium in which the light propagates in can be air or a material medium with an effective refractive index of propagation “n”. In the case of free space, “n” is the material refractive index. In the case of a planar waveguide, “n” is the effective refractive index of propagation within the planar waveguide.
The relation between θ1, θ2, and the initial groove spacing d is given by the grating formula,d*(Sin(θ2)−Sin(θ1))=m*λc/n  (0)
where m is the diffraction order, n is the effective refractive index of propagation of the medium, λc is the center of the operation wavelength. This grating formula is a so-called far-field approximation, which is valid only when S1 and S2 are much larger than d.
Initial groove positions are X0=(0,0), X1=(d, R−(R2−d2)1/2) and X−1=(−d, R−(R2−d2)1/2). These three initial grooves with position vectors X0, X1, and X−1, are located on a circle of radius R and have the initial groove spacing of d along a chord (CD in FIG. 3) parallel to the grating tangent (AB in FIG. 3). The grating tangent is a line segment tangent to the grating-center curve.
All other grooves, specified by its position vector Xi's, are located on the same circle of radius R defined by the initial three groove positions X, X, and X−1. Xi's are also equally spaced along a chord that is parallel to the tangent of the grating-center curve. In other words, the projection of the displacement vector Xi−Xi−1 on this chord always has the same length. Specifically, the position vectors of these grooves can be written as Xi=(d*i, R−(R2−(d*i)2)1/2), and X−i=(−d*i, R−(R2−(d*i)2)1/2), where “*” denotes numerical multiplication and “i” is a positive integer denoting the ith groove so that “i” can take any of the values 0, 1, 2, 3, 4, . . . etc.
For example, if the radius of curvature at the grating center is r=100 μm, the Rowland circle, where the entrance slit and the detector are located, has the radius of 50 μm. Here, we assume that tangent line at the grating-center curve is parallel to the x-axis. Since the Rowland circle is tangent to the grating-center curve, it circles by passing both the grating center X0=(0,0) and a point (0, 50). If the angle of the entrance slit is θ1=45°, the distance of the entrance slit to the grating center is S1=R*Cos(θ1)=70.71 μm. In terms of (x,y)-coordinate, the entrance slit is located at (−50, 50). It is well-known that grating is more efficient if the propagation direction of the diffracted light from the grating is nearly parallel and opposite to the propagation direction of the input beam. Such a scheme is known as Littrow configuration and is widely used for a high-efficiency spectrometer. A Littrow configuration in the Rowland design will be equivalent to having the angle of detector being almost equal to the angle of the entrance slit, i.e., θ1≈θ2. Besides being at the Littrow configuration, the groove spacing d at the grating center has to be properly chosen so that it satisfies grating formula Eq. 0. For example, when the center wavelength is 1550 nm and the angle of entrance slit is θ1=45°, the diffraction order of m=12 of a grating with the groove spacing of d=4.2 μm at its center propagate toward a detector located at θ2=37.37°, which is close to the Littrow configuration. The detector location can be fine tuned by changing the initial groove spacing d. Lower the groove spacing d, larger the detector angle θ2. For the groove spacing d=4.2 μm and radius of curvature R=100 μm, the initial three positions of grooves are X0=(0,0), X1=(4.2, 0.088) and X−1=(−4.2, 0.088).
In the Rowland design, other grooves are located such that their spacing is the same along a chord parallel to the grating tangent at the center. Therefore, the position vectors of other grooves are Xi=(d*i, R−(R2−(d*i)2)1/2)=(4.2*i, 100−(1002−(4.2*i)2)1/2), and X−1=(−d*i, R−(R2−(d*i)2)1/2)=(−4.2*i, 100−(1002−(4.2*i)2)1/2). The position vectors of the grooves are listed in the following table for the case of Rowland design with R=100 μm, d=4.2 μm, m=12, θ1=45°, and θ2=37.37° for an operation wavelength of λc=1550 nm.
TABLE 1X−13(−54.6, 16.221)X−12(−50.4, 13.630)X−11(−46.2, 11.312)X−10(−42, 9.248)X−9(−37.8, 7.419)X−8(−33.6, 5.814)X−7(−29.4, 4.419)X−6(−25.2, 3.227)X−5(−21, 2.230)X−4(−16.8, 1.421)X−3(−12.6, 0.797)X−2(−8.4, 0.353)X−1(−4.2, 0.088)X0(0, 0)X1(4.2, 0.088)X2(8.4, 0.353)X3(12.6, 0.797)X4(16.8, 1.421)X5(21, 2.230)X6(25.2, 3.227)
The advent in Dense Wavelength Division Multiplexing (DWDM) optical communication networks, however, requires that the multiple wavelengths in an optical fiber to be analyzed by spectral analysis devices that are much smaller in size than that of the current grating spectrometer. The challenge is to circumvent the current limitation in grating spectrometer design and fabrication methods. As discussed above, the current design basically cannot achieve the Resolution-Size factor (RS) much smaller than about 10. While several current technologies are capable of using planar waveguide technologies to make grating based spectrometers on a single silica or semiconductor substrate, they are still not able to achieve RS much smaller than 10 due to the basic limitations of the grating spectrometer design. Achieving a smaller RS factor is important for combining or integrating high-resolution grating spectrometers or wavelength multiplexer (Mux) and demultiplexer (deMux) with various photonic devices (such as lasers, modulators, or detectors in a compact module or silica/silicon/semiconductor wafer).
These wavelength-division-multiplexed (WDM) integrated photonic devices or modules would be of great importance for applications to Dense Wavelength Division Multiplexed (DWDM) networks. The costs of these integrated WDM devices are typically proportional to their sizes. The wavelength dispersion elements, such as the grating spectrometer or other form of wavelength filters and wavelength Mux/deMux, are typically about 100 times larger in size than any other photonic devices in the module or wafer. In order to reduce their costs substantially, it is desirable to reduce the size of these wavelength dispersion elements to as small a size as possible.
Thus, it is desirable to have grating based spectrometers that have an RS factor of less than 10. It is also desirable to reduce the size, and hence the cost, of integrated WDM devices that are used in DWDM networks. The present invention discloses such a device and a method for making the same.